GATE ME 2015 Set 2 | Transform Theory Question 5 | Engineering Mathematics

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GATE ME 2015 Set 2

MCQ (Single Correct Answer)

-0.3

Laplace transform of $$\cos \left( {\omega t} \right)$$ is

$${s \over {{s^2} + {\omega ^2}}}$$

$${\omega \over {{s^2} + {\omega ^2}}}$$

$${s \over {{s^2} - {\omega ^2}}}$$

$${\omega \over {{s^2} - {\omega ^2}}}$$

GATE ME 2015 Set 2

MCQ (Single Correct Answer)

-0.3

The Laplace transform of $${e^{i5t}}$$ where $$i = \sqrt { - 1} ,$$

$${{s - 5i} \over {{s^2} - 25}}$$

$${{s + 5i} \over {{s^2} + 25}}$$

$${{s + 5i} \over {{s^2} - 25}}$$

$${{s - 5i} \over {{s^2} + 25}}$$

GATE ME 2015 Set 1

MCQ (Single Correct Answer)

-0.3

The Laplace Transform of $$f\left( t \right) = {e^{2t}}\sin \left( {5t} \right)\,u\left( t \right)$$ is

$${5 \over {{s^2} - 4s + 29}}$$

$${5 \over {{s^2} + 5}}$$

$${{s - 2} \over {{s^2} - 4s + 29}}$$

$${5 \over {s + 5}}$$

GATE ME 2014 Set 4

MCQ (Single Correct Answer)

-0.3

Laplace transform of $$\cos \,\left( {\omega t} \right)$$ is $${s \over {{s^2} + {\omega ^2}.}}$$. The Laplace transform of $${e^{ - 2t}}\,\cos \left( {4t} \right)$$ is

$${{s - 2} \over {{{\left( {s - 2} \right)}^2} + 16}}$$

$${{s + 2} \over {{{\left( {s - 2} \right)}^2} + 16}}$$

$${{s - 2} \over {{{\left( {s + 2} \right)}^2} + 16}}$$

$${{s + 2} \over {{{\left( {s + 2} \right)}^2} + 16}}$$

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GATE ME Subjects

Engineering Mechanics

Engineering Mechanics Static and Dynamics

Strength of Materials

Springs Pure Bending Stresses In Beams Simple Stress and Strain Complex Stresses Moment of Inertia Deflection of Beams Shear Force and Bending Moment Torsion Thin Cylinders Columns and Struts Strain Energy Method

Theory of Machines

Vibrations Gears and Gear Trains Flywheel Analysis of Plane Mechanisms

Engineering Mathematics

Linear Algebra Vector Calculus Probability and Statistics Differential Equations Transform Theory Calculus Complex Variable Numerical Methods

Machine Design

Bolted Riveted and Welded Joints Design For Static Loading Design of Brakes and Clutches Design of Spur Gears Design of Bearings Fatigue Strength

Fluid Mechanics

Fluid Properties Boundary Layer Turbulent Flow Fluid Dynamics Laminar Flow Fluid Kinematics Fluid Statics

Turbo Machinery

Heat Transfer

Conduction Fin Design and Transient Heat Conduction Convection Radiation Heat Exchangers

Thermodynamics

Calculation of Work and Heat Entropy and Irreversibility Properties of Pure Substances Basic Concepts and Zeroth Law First Law of Thermodynamics Rankine Cycle Availability Second Law of Thermodynamics

Production Engineering

Metrology and Inspection Sheet Metal Forming Processes Welding Process Metal Forming Metal Cutting Advance Machine Tools Machining Casting

Industrial Engineering

Queuing Production Planning and Control Line Balancing Forecasting Linear Programming Assignment Pert and Cpm Inventory Control Transportation Scheduling

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability